A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of 60∘. After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30∘. Find the distance the boat has to travel to reach a point that is exactly above the submarine. [Tan 30∘=0.57, tan 60∘=1.73]
86.2 m
In the given figure, the person is standing on the boat at A and the submarine moves from B to C.
The boat has to travel distance AD to reach D, a point which is exactly above the submarine.
In △ADCtan 30∘=CDAD0.57=CDADCD=0.57 AD (i)
In △ADBtan 60∘=BDAD1.73=BDADBD=1.73AD(ii)
Now, we can observe that CB=BD−CD100=1.73 AD−0.57AD100=1.16ADAD=86.2 m
Hence, the boat has to travel 86.2 m to reach a point which is exactly above the submarine.